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Since its invention HyperLogLog has become the standard algorithm for approximate distinct counting. Due to its space efficiency and suitability for distributed systems, it is widely used and also implemented in numerous databases. This work presents UltraLogLog, which shares the same practical properties as HyperLogLog. It is commutative, idempotent, mergeable, and has a fast guaranteed constant-time insert operation. At the same time, it requires 28% less space to encode the same amount of distinct count information, which can be extracted using the maximum likelihood method. Alternatively, a simpler and faster estimator is proposed, which still achieves a space reduction of 24%, but at an estimation speed comparable to that of HyperLogLog. In a non-distributed setting where martingale estimation can be used, UltraLogLog is able to reduce space by 17%. Moreover, its smaller entropy and its 8-bit registers lead to better compaction when using standard compression algorithms. All this is verified by experimental results that are in perfect agreement with the theoretical analysis which also outlines potential for even more space-efficient data structures. A production-ready Java implementation of UltraLogLog has been released as part of the open-source Hash4j library.

White matter (WM) tract segmentation is a crucial step for brain connectivity studies. It is performed on diffusion magnetic resonance imaging (dMRI), and deep neural networks (DNNs) have achieved promising segmentation accuracy. Existing DNN-based methods use an annotated dataset for model training. However, the performance of the trained model on a different test dataset may not be optimal due to distribution shift, and it is desirable to design WM tract segmentation approaches that allow better generalization of the segmentation model to arbitrary test datasets. In this work, we propose a WM tract segmentation approach that improves the generalization with scaled residual bootstrap. The difference between dMRI scans in training and test datasets is most noticeably caused by the different numbers of diffusion gradients and noise levels. Since both of them lead to different signal-to-noise ratios (SNRs) between the training and test data, we propose to augment the training scans by adjusting the noise magnitude and develop an adapted residual bootstrap strategy for the augmentation. To validate the proposed approach, two dMRI datasets were used, and the experimental results show that our method consistently improved the generalization of WM tract segmentation under various settings.

The shift towards electrification and autonomous driving in the automotive industry results in more and more automotive wire harnesses being installed in modern automobiles, which stresses the great significance of guaranteeing the quality of automotive wire harness assembly. The mating of connectors is essential in the final assembly of automotive wire harnesses due to the importance of connectors on wire harness connection and signal transmission. However, the current manual operation of mating connectors leads to severe problems regarding assembly quality and ergonomics, where the robotized assembly has been considered, and different vision-based solutions have been proposed to facilitate a better perception of the robot control system on connectors. Nonetheless, there has been a lack of deep learning-based solutions for detecting automotive wire harness connectors in previous literature. This paper presents a deep learning-based connector detection for robotized automotive wire harness assembly. A dataset of twenty automotive wire harness connectors was created to train and evaluate a two-stage and a one-stage object detection model, respectively. The experiment results indicate the effectiveness of deep learning-based connector detection for automotive wire harness assembly but are limited by the design of the exteriors of connectors.

The discovery of scientific formulae that parsimoniously explain natural phenomena and align with existing background theory is a key goal in science. Historically, scientists have derived natural laws by manipulating equations based on existing knowledge, forming new equations, and verifying them experimentally. In recent years, data-driven scientific discovery has emerged as a viable competitor in settings with large amounts of experimental data. Unfortunately, data-driven methods often fail to discover valid laws when data is noisy or scarce. Accordingly, recent works combine regression and reasoning to eliminate formulae inconsistent with background theory. However, the problem of searching over the space of formulae consistent with background theory to find one that fits the data best is not well-solved. We propose a solution to this problem when all axioms and scientific laws are expressible via polynomial equalities and inequalities and argue that our approach is widely applicable. We further model notions of minimal complexity using binary variables and logical constraints, solve polynomial optimization problems via mixed-integer linear or semidefinite optimization, and prove the validity of our scientific discoveries in a principled manner using Positivestellensatz certificates. Remarkably, the optimization techniques leveraged in this paper allow our approach to run in polynomial time with fully correct background theory, or non-deterministic polynomial (NP) time with partially correct background theory. We demonstrate that some famous scientific laws, including Kepler's Third Law of Planetary Motion, the Hagen-Poiseuille Equation, and the Radiated Gravitational Wave Power equation, can be derived in a principled manner from background axioms and experimental data.

Generalized metric spaces are obtained by weakening the requirements (e.g., symmetry) on the distance function and by allowing it to take values in structures (e.g., quantales) that are more general than the set of non-negative real numbers. Quantale-valued metric spaces have gained prominence due to their use in quantitative reasoning on programs/systems, and for defining various notions of behavioral metrics. We investigate imprecision and robustness in the framework of quantale-valued metric spaces, when the quantale is continuous. In particular, we study the relation between the robust topology, which captures robustness of analyses, and the Hausdorff-Smyth hemi-metric. To this end, we define a preorder-enriched monad $\mathsf{P}_S$, called the Hausdorff-Smyth monad, and when $Q$ is a continuous quantale and $X$ is a $Q$-metric space, we relate the topology induced by the metric on $\mathsf{P}_S(X)$ with the robust topology on the powerset $\mathsf{P}(X)$ defined in terms of the metric on $X$.

We address the challenge of enhancing navigation autonomy for planetary space rovers using reinforcement learning (RL). The ambition of future space missions necessitates advanced autonomous navigation capabilities for rovers to meet mission objectives. RL's potential in robotic autonomy is evident, but its reliance on simulations poses a challenge. Transferring policies to real-world scenarios often encounters the "reality gap", disrupting the transition from virtual to physical environments. The reality gap is exacerbated in the context of mapless navigation on Mars and Moon-like terrains, where unpredictable terrains and environmental factors play a significant role. Effective navigation requires a method attuned to these complexities and real-world data noise. We introduce a novel two-stage RL approach using offline noisy data. Our approach employs a teacher-student policy learning paradigm, inspired by the "learning by cheating" method. The teacher policy is trained in simulation. Subsequently, the student policy is trained on noisy data, aiming to mimic the teacher's behaviors while being more robust to real-world uncertainties. Our policies are transferred to a custom-designed rover for real-world testing. Comparative analyses between the teacher and student policies reveal that our approach offers improved behavioral performance, heightened noise resilience, and more effective sim-to-real transfer.

This paper addresses the electromagnetic inverse scattering problem of determining the location and shape of anisotropic objects from near-field data. We investigate both cases involving the Helmholtz equation and Maxwell's equations for this inverse problem. Our study focuses on developing efficient imaging functionals that enable a fast and stable recovery of the anisotropic object. The implementation of the imaging functionals is simple and avoids the need to solve an ill-posed problem. The resolution analysis of the imaging functionals is conducted using the Green representation formula. Furthermore, we establish stability estimates for these imaging functionals when noise is present in the data. To illustrate the effectiveness of the methods, we present numerical examples showcasing their performance.

Recent years have witnessed the enormous success of low-dimensional vector space representations of knowledge graphs to predict missing facts or find erroneous ones. Currently, however, it is not yet well-understood how ontological knowledge, e.g. given as a set of (existential) rules, can be embedded in a principled way. To address this shortcoming, in this paper we introduce a framework based on convex regions, which can faithfully incorporate ontological knowledge into the vector space embedding. Our technical contribution is two-fold. First, we show that some of the most popular existing embedding approaches are not capable of modelling even very simple types of rules. Second, we show that our framework can represent ontologies that are expressed using so-called quasi-chained existential rules in an exact way, such that any set of facts which is induced using that vector space embedding is logically consistent and deductively closed with respect to the input ontology.

Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.

Image segmentation is considered to be one of the critical tasks in hyperspectral remote sensing image processing. Recently, convolutional neural network (CNN) has established itself as a powerful model in segmentation and classification by demonstrating excellent performances. The use of a graphical model such as a conditional random field (CRF) contributes further in capturing contextual information and thus improving the segmentation performance. In this paper, we propose a method to segment hyperspectral images by considering both spectral and spatial information via a combined framework consisting of CNN and CRF. We use multiple spectral cubes to learn deep features using CNN, and then formulate deep CRF with CNN-based unary and pairwise potential functions to effectively extract the semantic correlations between patches consisting of three-dimensional data cubes. Effective piecewise training is applied in order to avoid the computationally expensive iterative CRF inference. Furthermore, we introduce a deep deconvolution network that improves the segmentation masks. We also introduce a new dataset and experimented our proposed method on it along with several widely adopted benchmark datasets to evaluate the effectiveness of our method. By comparing our results with those from several state-of-the-art models, we show the promising potential of our method.